The Remainder Theorem: Suppose p is a polynomial of degree at least 1 The proof of The Factor Theorem is a consequence of what we already know
If f(x) is a polynomial and f(a) = 0, then (x–a) is a factor of f(x) Proof of the factor theorem Let's start with an example Consider 4 8 5
Irreducible quadratic: a quadratic expression which cannot be written as a product of two linear factors using the set of real numbers, R, e g , 2 + 1 = 0 In
Factor theorem state with proof examples and solutions factorise the Polynomials Maths Mutt Solution Here feel some examples of using the Factor Theorem
In this section, we will learn to use the remainder and factor theorems to factorise and to solve polynomials that are of degree higher than 2 Before doing so,
(Refer to page 506 in your textbook for more examples ) Example 5: Use both long and short (synthetic) division to find the quotient and remainder for the
4 2 8 - The Factor Theorem 4 2 - Algebra - Solving Equations Leaving Certificate Mathematics Higher Level ONLY 4 2 - Algebra - Solving Equations
q is a factor of the leading coefficient n a Example 1: List all possible rational zeros given by the Rational Zeros Theorem of P(x) = 6x
The Remainder Theorem follows immediately from the definition of polynomial division: etc, this can be highly effective; try, for example, evaluating x6
the following are all examples of quadratic equations o 2 2 ? 3 ? 5 = 0 we will use the Zero Factor Theorem to solve quadratic equations
The Remainder Theorem for divisor ( − ) From the above examples, we saw that a polynomial can be expressed as a product of the quotient and the
the following are all examples of quadratic equations o 2 2 − 3 − 5 zero, and factor that polynomial, we can use the Zero Factor Theorem to solve it
1 3 1 THE REMAINDER THEOREM AND THE FACTOR THEOREM Definition: Example 1 Is 0 a zero of ( ) 1 2 3 + − = xx xP I DIVISION OF POLYNOMIALS